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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1007/bf00195738

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1573-7586

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A combinatorial problem related to sparse systems

Authors: Peter Horak Igor Semaev Zsolt Tuza
Publish Date: 2016/11/02
Volume: 85, Issue: 1, Pages: 129-144
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Abstract

Nowadays sparse systems of equations occur frequently in science and engineering In this contribution we deal with sparse systems common in cryptanalysis Given a cipher system one converts it into a system of sparse equations and then the system is solved to retrieve either a key or a plaintext Raddum and Semaev proposed new methods for solving such sparse systems common in modern ciphers which are combinations of linear layers and small Sboxes It turns out that the solution of a combinatorial MaxMinMax problem provides an upper bound on the average computational complexity of those methods In this paper we initiate the study of a linear algebra variation of the MaxMinMax problem The complexity bound proved in this paper significantly overcomes conjectured complexity bounds for Gröbner basis type algorithmsThe authors are indebted to Noga Alon for discussions on expanders and on probabilistic methods which lead to an improvement of the lower bound in Theorem 1 and to Øyvind Ytrehus for a discussion on the Gilbert–Varshamov bound Research of P Horak was supported in part by a Grant from SIAS University of Washington Tacoma Research of P Horak and I Semaev was supported in part by a Grant SPIRE Program in 2013–2015 from University of Bergen Research of I Semaev was also partly supported by the EEA Grant SK06IV01001 and the State Budget of the Slovak Republic from the EEA Scholarship Programme Slovakia Research of Zs Tuza was supported in part by the Grant TÁ MOP422B15/1/KONV20150004


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Other Papers In This Journal:

  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. The Diffie–Hellman problem and generalization of Verheul’s theorem
  16. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  17. Improved lower bounds on sizes of single-error correcting codes
  18. Some results concerning cryptographically significant mappings over GF(2 n )
  19. A note on the reducibility of binary affine polynomials
  20. Primitive normal bases for quartic and cubic extensions: a geometric approach
  21. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  22. Some cyclic codes of length 2 p n
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications

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